Am I committing a sin by leaving a young man and a young woman to talk for a long time alone on my apartment balcony, and what is the way to rectify this to avoid embarrassment?

Hosting male and female colleagues in one residence is an unlawful mixing (ikhtilat muharram) due to the prohibitions that result from it. What occurred between the young man and the young woman was a reprehensible act (munkar) that should have been prevented; otherwise, the host would be complicit in the sin. One should not remain silent about a reprehensible act to please people; for whoever seeks Allah's pleasure by incurring people's displeasure, Allah will spare him the trouble of people. And whoever seeks people's pleasure by incurring Allah's displeasure, Allah will entrust him to people.